Question: Which of the following numbers is a factor of 108? ${6,7,10,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $108$ by each of our answer choices. $108 \div 6 = 18$ $108 \div 7 = 15\text{ R }3$ $108 \div 10 = 10\text{ R }8$ $108 \div 13 = 8\text{ R }4$ $108 \div 14 = 7\text{ R }10$ The only answer choice that divides into $108$ with no remainder is $6$ $ 18$ $6$ $108$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $108$ $108 = 2\times2\times3\times3\times3 6 = 2\times3$ Therefore the only factor of $108$ out of our choices is $6$. We can say that $108$ is divisible by $6$.